Tribute to Endre Csáki and Pál Révész

Summary This article provides a glimpse of some of the highlights of the joint work of Endre Csáki and Pál Révész since 1979. The topics of this short exploration of the rich stochastic milieu of this inspiring collaboration revolve around Brownian motion, random walks and their long excursions, local times and additive functionals, iterated processes, almost sure local and global central limit theorems, integral functionals of geometric stochastic processes, favourite sites--favourite values and jump sizes for random walk and Brownian motion, random walking in a random scenery, and large void zones and occupation times for coalescing random walks.     

Path properties of l_p-valued Gaussian random fields

General limit theorems are established for l~p-valued Gaussian random fields indexed by a multidimensional parameter,which contain both almost sure moduli of continuity and limits of large increments for the l~p-valued Gaussian random fields under(?)explicit conditions.     

Theoretical implications involved in the DDRP method

The aim of this paper is to prove that safe success in finding reaction paths (RPs) can only be expected from global path-determining methods. Some extensions of the mathematical arguments leading to the introduction of the DDRP (dynamically defined reaction path) method have been sketched. Four cases involving relaxation of analyticity, variability of the gradient field, minimum energy (reaction) paths (MEPs) and golf pocket holes on the potential energy surface (PES), and the rather strange consequences of the main theorem of the DDRP method giving a rigorous mathematical basis to chemical intuition in reaction kinetics have been discussed. The discussions show that the DDRP method - when changing the conditions and parameters - may, in essence, involve all other global methods. It has been shown that the DDRP method works in a stable way even for non-analytic though smooth energy functions; moreover, the gradient field can be replaced by other vector fields resulting in better convergence to the reaction path. As a by-product, the question of the existence of MEPs can safely be handled and golf pocket holes are constructed on the PES in order to prove that local methods have chance to search faithfully the RPs in complicated systems only if the energy function can be restored from its arbitrarily small pieces.This work was presented in parts at the 8th International Congress of Quantum Chemistry, Prague, Czech Republic, June 19–23,1994; Addendum to the Book of Abstracts of the 8ICQC: P/I-129.     

Nuclear gluon shadowing via continuum lepton pairs inp+A collisions at\sqrt s = 200 A GeV

The dilepton spectra from open charm decay inp+A reactions at $\sqrt s = 200$ AGeV are proposed to constrain gluon shadowing in nuclei. We show that the required measurements are feasible at RHIC.     

Synthesis of vinca alkaloids and related compounds. 100. Stereoselective oxidation reactions of compounds with the aspidospermane and quebrachamine ring system. First synthesis of some alkaloids containing the epoxy ring

The first syntheses of the alkaloids (-)-mehranine (3), (+)-voaphylline/conoflorine (4), (+)-N(a)-methylvoaphylline/hecubine (5), and (-)-lochnericine (2) were achieved by stereoselective epoxidation starting from (-)-tabersonine (1), through intermediates with the aspidospermane and quebrachamine skeleton.     

An algorithm for determining dynamically defined reaction paths (DDRP)

Summary A numerically stable and well-parallelizable curve variational algorithm is described for determining tangent curves of vector fields between two given stationary points. In particular, the method is suitable for finding reaction paths and saddle points on potential energy hypersurfaces (PHS). The stability of the procedure is illustrated by an artificial mathematical function, showing phases of following the reaction on the PHS.Dedicated to Professor Zoltán G. Szabó, the great teacher and scientist in reaction kinetics and in many other fields of physical chemistry, on his 84th birthday.     

Rate constant of unimolecular decomposition of the radical (CH3)2juvyCCH(CH3)2

The energy of activation of CH ₃ ^. radical rupture from the radical (CH₃)₂juvyCCH(CH₃)₂ is 142.2 kJ mol^–1; the selfcombination rate constant is k_c {(CH₃)₂juvyCCH(CH₃)₂}=10^7.3 dm³ mol^–1 s^–1.

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CH ₃ ^. (CH₃)₂juvyCCH(CH₃)₂ 142,2 /, k_c {(CH₃)₂juvyCCH(CH₃)₂}=10^{7,3 3–1 –1}.

     

Effects of different alkali metal ions on the cationization of poly(ethylene glycol)s in matrix-assisted laser desorption/ionization mass spectrometry: a new selectivity parameter

The cationization of poly(ethylene glycol)s, PEG 4000 and PEG 6000, under matrix-assisted laser desorption/ionization conditions was studied by using different concentration ratios of the sodium ion, as the reference ion, and another alkali metal ion (Li(+), K(+), Rb(+), Cs(+)). A linear correlation was found between the intensity ratio of the sodiated PEGs and PEGs cationized with alkali metal ions versus the initial concentration ratio of sodium and alkali metal ions. The slopes of these straight lines are proposed as a novel selectivity ratio for the ionization process. The intensity distribution of the cationized PEGs was also investigated. It was found that the cationized oligomers follow Poisson statistics. The M(n) and M(w) values were also evaluated. An explanation for the observed effects is given.     

Synthesis and characterization of molybdenum oxo complexes of two tripodal ligands: reactivity studies of a functional model for molybdenum oxotransferases

Reaction of the tetradentate ligand N-(2-hydroxybenzyl)-N,N-bis(2-pyridylmethyl)amine (L-OH) with MoO2Cl2 in methanol in the presence of NaOMe and PF6- results in the formation of [MoO2(L-O)]PF6. Similarly, the reaction of N-(2-mercaptobenzyl)-N,N-bis(2-pyridylmethyl)amine (L-SH) with MoO2(acac)2 leads to the formation of [MoO2(L-S)]+. The dioxo-molybdenum complex [MoO2(L-O)]+ reacts with phosphines in methanol to afford phosphine oxides and an air-sensitive molybdenum complex, tentatively identified as [Mo(IV)O(L-O)(OCH3)]. The latter complex is capable of reducing biological oxygen donors such as DMSO or nitrate, thereby mimicking the activity of DMSO reductase and nitrate reductase. Reaction of [MoO2(L-O)]PF6 with PPh3 in other solvents than methanol leads to the formation of the Mo(V) dimer [(L-O)OMo(micro-O)MoO(L-O)](PF6)2. The crystal structures of [MoO2(L-O)]PF6 and the micro-oxo bridged dimer are presented.